Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠A1 is smaller than ∠A2.)
b = 121, c = 162, ∠B = 48°

The number of biology textbooks sold =  156

The number of psychology textbooks sold = 95

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Let x be the number of biology textbooks sold. Then, the number of psychology textbooks sold was x - 61.

The combined total of the two types of textbooks sold was 251, so we can write an equation:

x + (x - 61) = 251

Expanding the right side:

2x - 61 = 251

Adding 61 to both sides:

2x = 312

Dividing both sides by 2:

x = 156

the number of psychology textbooks sold =  x - 61

                                                                      =  156 - 61

                                                                      =  95

So, 156 biology textbooks were sold and 95 psychology textbooks were sold.

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The values of the terms, a₁, a₂, and a₁₀ of the sequence are;

(a) a₁ = 1, a₂ = 1/2, a₁₀ = 1/10

(b)  [tex]\lim\limits_{n\to {\infty}}[/tex] aₙ = 0

A sequence is an ordered collection of objects such as numbers in which repetition of the object is possible, and the objects (or numbers) are referred to as the terms of the sequence.  

The sequence, [tex]\{a_n\}^\infty_{n = 1}[/tex] with values, aₙ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{n + 1}} }[/tex]

(a) a₁ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{1 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^2} } = -[\frac{1}{x} ]^{\infty}_1[/tex]

[tex]-[\frac{1}{x} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{1} ) = 0 + 1 = 1[/tex]

Therefore; a₁ = 1

a₂ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{2 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^3} } = -[\frac{1}{2\cdot x^2} ]^{\infty}_1[/tex]

[tex]-[\frac{1}{2\cdot x} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{2 \times 1} ) = 0 + \frac{1}{2} = \frac{1}{2}[/tex]

Therefore; a₂ = 1/2

a₁₀ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{10 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^{11}} } = [-\frac{1}{10\cdot x^{10}} ]^{\infty}_1[/tex]

[tex][-\frac{1}{10\cdot x^{10}} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{10\times 1} ) = 0 + \frac{1}{10} = \frac{1}{10}[/tex]

Therefore; a₁₀ = 1/10

b) The limit, [tex]\lim \limits_{n\to \infty} a_n[/tex] can be evaluated as follows;

aₙ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{n+1} } } \, dx[/tex]

[tex]\int\limits^{\infty}_1 {\frac{dx}{x^{n+1} } } \, dx = [-\frac{1}{n\cdot x^n} ]^{\infty}_1 = -\frac{1}{n\times \infty } - (-\frac{1}{n\times 1^n} )= \frac{1}{n}[/tex]

aₙ = 1/n

Therefore;

[tex]\lim \limits_{n\to \infty} a_n = \frac{1}{\infty}[/tex] = 0

[tex]\lim\limits_{n\to {\infty}} a_n[/tex] = 0

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The calculation of uncertainty depends on various factors, including the method used, the distribution of the data, and the number of data points. In some cases, the calculated uncertainty may be lower than the actual deviation of the data, especially if the data is not normally distributed or if the number of data points is small.

It's also important to keep in mind that uncertainty is a measure of the spread of the data, not the absolute deviation from the mean. In other words, if the data is tightly clustered around the mean, the calculated uncertainty will be low, even if the maximum deviation from the mean is relatively high.

If you think your calculated uncertainty is not accurately representing the spread of your data, you may want to consider using a different method for calculating uncertainty, or checking the underlying assumptions of the method you are using to ensure that it is appropriate for your data set.

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The uncertainty of a group of data represents the range of possible values that the data could reasonably have and is not expected to exceed the actual mathematical value of the data.

The uncertainty of a group of data is determined by factors such as measurement error and natural variability in the data & represents the range of possible values that the data could reasonably have. It is not expected to exceed the actual mathematical value of the data because the mathematical value represents the best estimate of the true value based on the available data.

The uncertainty is a measure of the limitations and potential sources of error in the data and helps to quantify the level of confidence that can be placed in the mathematical value.

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The original purchase price of the car before any of the discounts and taxes is,

⇒  $15,024

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

There is a 12% discount because of the Happy Easter Sale and another 5% discount because the purchaser is a valued customer. After these discounts the GST increases the price by 10%.

Here, the customer paid $14 000.

Now, Let the original price = x

Hence, We can formulate;

⇒ x - (12% of x) - 5% of x + 10% of x = 14,000

⇒ x - 12x/100 - 5x/100 + 10x/100 = 14,000

⇒ (100x - 12x - 5x + 10x) / 100 = 14,000

⇒ 93x/100 = 14,000

⇒ 93x = 1400000

⇒ x = $15,024

Thus, The original purchase price of the car before any of the discounts and taxes is,

⇒  $15,024

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To design the table, you could create a "Sports" table and a "Patient-Sport" table with the following fields:

Sports table:                                      Patient-Sport table:

SportID (primary key)                        PatientID (foreign key)

SportName                                        SportID (foreign key)

A database is a collection of organized data stored and retrieved electronically. It is designed to allow efficient storage, retrieval, manipulation, and management of large amounts of data. Databases can be used to store information such as text, numbers, images, and other media. The data in a database is typically organized into tables, which are made up of rows and columns. Each row represents a single record, and each column represents a field of information within that record. There are many different types of databases, including relational databases, NoSQL databases, and in-memory databases, and they are used in a wide range of applications, such as online retail, finance, healthcare, and more.

The Patient-Sport table is used to connect the patient to the sport they are playing. This allows for multiple sports to be assigned to a single patient. In this way, you can track the sports played by each patient, while still maintaining the relationships between the patient and their data in the other tables.

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Step-by-step explanation:

You would need to start by finding how many students is 1/5 of them

So to find this out you would take 70 and divided it by 5

So 70/5 = 14

Take 70 and subtract 14 to get 56

Next find what 1/7 is

So 56/7 = 8

But because it’s 2 sevenths take the 1/7 and multiply by 2

8 x 2 = 16

So
Take the 56 and subtract 16 to get 40

To find the fraction form it would be

40/70 students

Just simplify now

4/7

Step-by-step explanation:

day 1

70*1/5= 14

70-14 = 56

day 2

2/7 * 56= 16

16+14 = 30.

Remaining students = 70 - 30 = 40

The solution of a system of equations can be determined by dividing the coefficients of variables.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Solution of system of equations :-

Let the two system of equations be

a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

1) Unique solution or one solution :-

The solution of the system of equations will be unique when,

a₁ / a₂ ≠ b₁ / b₂

2) Infinite solutions :-

The solution of the system of equations will have infinitely many solutions when,

a₁ / a₂ = b₁ / b₂ = c₁ / c₂

3) No solution :-

The solution of the system of equations will have no solutions when,

a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂

Hence, the solution of a system of equations can be determined by dividing the coefficients of variables.

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i'm to lazy to bored trying to do my work and I'm also very dumm

The perimeter and area of the figure are 40.8 units and 110 square units respectively.

From the question, we have the following parameters that can be used in our computation:

The figure

Using the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²],

where d is the distance between the points (x₁, y₁) and (x₂, y₂).

So, we have

AB = √[(8-8)² + (9-2)²] = 7

BC = √[(3-8)² + (13-9)²] = 6.4

CD = √[(-3-3)² + (9-13)²] = 7.2

DE = √[(-3+3)² + (9-13)²] = 9

EA = √[(8+3)² + (2-0)²] = 11.2

DB = √[(8+3)² + (9-9)²] = 11

Perimeter = AB + BC + CD + DE + EA.

Perimeter = 7 + 6.4 + 7.2 + 9 + 11.2

Perimeter = 40.8 units.

The figure is observed to be a trapezium ABDE and a triangle BCD.

Triangle BCD have base length DB = 11 with height from C to DB equal to 4.

Trapezium ABDE have sides AB and DE parallel to each other, and height DB = 11.

area of triangle BCD = 1/2 × 11 × 4 = 22 square units

area of trapezium ABDE = 1/2 × (7 + 9) × 11 = 88 square units

Total area ABCDE = 22 + 88

Total area = 110 square units

Hence, the perimeter and area of the figure are 40.8 units and 54 square units respectively.

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Answer:

20

Step-by-step explanation:

lets say width is 2x and the length is x

2x+x+2x+x=120

6x=120

x=20

thus, your answer is 20

Answer:

3000

Step-by-step explanation:

8 x 375 = 3000

Domain is all real numbers and Range is all real numbers less than or equal to -2.

A relation is a function if it has only One y-value for each x-value.

The given function is  f(x) = -x⁴+ 2x²-x-2

Domain is all real numbers.

Range is all real numbers less than or equal to -2.

Relative Maximum is the function does not have any relative maximums.

Relative Minimum(s): The function does not have any relative minimums.

End Behavior as x approaches infinity, f(x) approaches negative infinity. This can be seen by observing that the leading term in f(x),

-x⁴ grows much faster than the other terms as x increases, so the overall value of f(x) becomes more and more negative as x approaches infinity.

Hence, Domain is all real numbers and Range is all real numbers less than or equal to -2.

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Answer:

1.71 pounds of sugar per dollar.

Step-by-step explanation:

To calculate how many pounds of sugar Keisha got per dollar, we divide the total amount of sugar by the total amount of money spent. In this case, she bought 12 pounds of sugar for $7, so we divide 12 by 7:

12 ÷ 7 = 1.71

So, Keisha got 1.71 pounds of sugar per dollar.

The measure of side MK is 103.3.

To find the length of side MK, we need to use the concept of similar triangles. Similar triangles have the same shape but may be different sizes. In this case, the ratio of corresponding sides is the same.

Now, we can use the fact that the ratio of corresponding sides is the same for both triangles:

JI/JH = ML/MK

16/29 = 57/x

cross-multiply the expression, we get

16x = 57 × 29

x = (57 × 29)/16

x = 103.3125

Therefore the measure of side MK is 103.3 to the nearest tenth place.

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The expression - 7 meters represents the 7 meters in the west direction.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

If 20km represents 20 km due east.

We know that the opposite of the east direction will be the west direction.

Then we can conclude that if the east direction represents the positive values, then the west direction represents the negative value.

Then the expression - 7 meters represents the 7 meters in the west direction.

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The value of the expression is A = 4p ( 3 - 2 ) = 4p

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 12p - 8p   be equation (1)

On simplifying the equation , we get

Taking the common factor as 4p in the expression , we get

A = 4p ( 3 - 2 )

On further simplification , we get

A = 4p

Therefore , the value of A is 4p

Hence , the expression simplified is 4p

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Answer:

4.81 meters

Step-by-step explanation:

1 m = 100 cm

where m = meters

         cm = centimeters

481 centimeters need to be converted:

= 481 cm × [tex](\frac{1 m}{100 cm})[/tex]

The cm in the numerator and denominator will completely cancel each other out:

= [tex]\frac{481}{100}[/tex] m

= 4.81 meters

The missing words in the statement are mean and absolute deviation respectively.

The mean absolute deviation (MAD) is a measure of the average magnitude of the differences between individual values in a data set and the mean of the data set. It is calculated by first finding the absolute value of the difference between each data point and the mean, summing these absolute values, and then dividing by the number of data points. The resulting value provides a measure of the "typical" or average deviation of individual data points from the mean, without considering the direction of the deviation (positive or negative). The mean absolute deviation is often used as a summary statistic for data that is not normally distributed or when the variance or standard deviation are not meaningful.

The mean of the absolute deviation between the mean of the data set and the individual numbers in the data set is referred to as the mean absolute deviation (MAD).

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The difference of the data between the mean of the data set and individual numbers in the data set is called the deviation.

Mean Absolute Deviation (MAD) is a measure of the average distance between the values in a dataset and the mean of that data set. It is calculated by finding the absolute difference between each value and the mean, summing them, and dividing by the total number of values. MAD is commonly used as a way to describe the variability or dispersion of a set of data.

In other words, the mean absolute deviation (MAD) is the average distance between each data value and the mean of the data set.

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Jeremy should choose Model A.

From the question, we have the following parameters:

These mean that:

Model A = 2 * Backpack (x)

Model B = 15 + Backpack (x)

18 + Model A = 28 + Model B

As equations, we have

A = 2x

B = 15 + x

18 + A = 28 + B

So, we have

18 + 2x = 28 + 15 + x

Evaluate

x = 25

So, we have

A = 2 * 25 = 50

B = 15 + 25 = 40

Hence, he should choose model A

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The mapping above represents a function, since each number in Set A is mapped to only one number in Set B.

A relation represents a function when each input value is mapped to a single output value.

For the relation in this problem, we have that:

As there are no repeated inputs, the relation represents a function.

The diagram is given by the image presented at the end of the answer.

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The area of the surface to be covered by the label = 904.32 mm²

We know that the formula for the surface area of cylinder is:

A =  2πrh + 2πr²

where r is the radius of the cylinder and h is the height of the cylinder

Here, the dimensions of the cylindrical battery:

radius r = 4 millimeters

height h = 32 millimeters

Using the above formula of surface area of cylider, the area of the surface to be covered by the label would be,

A =  2πrh + 2πr²

A =  2πr(h + r)

A = 2π × 4 × (32 + 4)

A = 2 × 3.14 × 4 × 36

A = 904.32 mm²

Therefore, the required area is 904.32 mm²

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Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°

Explaining quadrilaterals?

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals' internal angles add up to a constant 360 degrees.

What is quadrilateral formula?

When the diagonal and the sum of the lengths of the perpendiculars drawn from the remaining two vertices are known, the area of the quadrilateral can be determined as follows Area of quadrilateral = (12) diagonal length sum of the lengths of the perpendiculars drawn from the remaining two vertices.

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The complete question is -

Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.

Cynthia's percent error in her fourth lab report was 4.38%.

Percent error is a measure of the accuracy of a numerical result, expressed as a percentage of the difference between the actual value and the calculated or measured value. It is calculated using the formula -

Percent Error = (|Actual value - Calculated value| / Actual value) * 100

In order to calculate Cynthia's percent error, we will use the formula:

Percent Error = (|Accepted Value - Measured Value| / Accepted Value) * 100%

For the mean of her four measured values (0.7325), the percent error would be:

Percent Error = (|0.77 - 0.7325| / 0.77) * 100% = 4.38%

So, the answer to be entered rounded to two decimal places is 4.38.

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For the first part of the question, here is my classification of each statement:

A) True. The domain of the function is all real numbers.

B) False. The range of the function is all real numbers.

C) False. The function has no x-intercepts.

D) False. The center of symmetry is (0, 0).

For the second part, the transformations performed from function f to function g are:

A) Function f is translated to the left 3 units.

For the third part, the transformations performed from function f to function g are:

A) Function f is translated to the right 3 units.

B) Function f is translated up 3 units.

For the last part, you would need to find the x and y-intercepts of the polynomial function, and plot them on the graph. The x-intercepts can be found by setting x=0 in the equation and solving for y. The y-intercept can be found by setting y=0 and solving for x. Once the intercepts are found, you can plot them on the graph and connect them to form the graph of the polynomial function.

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Problem 2

Problem 3

I cannot read your problem

Problem 4

[tex]f(x)=x^3+3x^2-4x-12\\0=x^3+3x^2-4x-12\\0=x^2(x+3)-4(x+3)\\0=(x^2-4)(x+3)\\0=(x-2)(x+2)(x+3)\\x_1=-3,\,x_2=-2,\,x_3=2[/tex]

Hence, the graph of the function would have points at (-3,0) (-2,0) and (2,0).

Answer:

k = 12

Step-by-step explanation:

Finding the unknown value:

    To find the value of 'k', isolate k

             2k + 36 = 6k - 12

                     2k = 6k - 12 - 36

                    2k = 6k - 48

                2k - 6k = -48

                      - 4k = -48

                          k = -48 ÷ (-4)

                          k = 12

[tex]y=2\frac{2}{3}+16[/tex] is the answer as it passes perpendicular and through point A

Answer:

Step-by-step explanation:

If there is a hole in the graph at x = -6, that means that there was initially an expression in both the numerator and the denominator that was the same, which is the hole very loosely defined. If the hole is at x = -6, then the factor for that solution is (x + 6). One of those has to be in both the numerator and denominator in order for them to cancel out. This is called a removeable discontinuity. Because the x-intercept is at x = 3, the factor for that zero is (x -3). That has to go in the numerator also. Our equation then for the rational function graphed is

[tex]y=\frac{(x+6)(x-3)}{(x+6)}[/tex] which FOILs to

[tex]y=\frac{x^2+3x-18}{x+6}[/tex]

The explicit formula for the given geometric series will be [tex]a_n = -4(3)^{n-1}[/tex].

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

Given that the geometric series is -4,-12,-36,-108. The formula for the nth term of the geometric progression will be written as:-

[tex]a_n = a_1(r)^{n-1}\\[/tex]

Here, r is the common ratio of the series. The value of the common ratio is r = -12 / -4 = 3.

The formula will be:-

[tex]a_n = a_1(r)^{n-1}\\[/tex]

[tex]a_n = -4(3)^{n-1}\\[/tex]

Therefore, the formula for the nth term will be [tex]a_n = -4(3)^{n-1}\\[/tex].

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